I think we are now going hyperbolic. If you add a feedback loop or two to a system experiencing exponential growth, it tends to kick it into a hyperbolic curve, truly explosive growth.
Increasing demand and flattening production have set oil prices on an exponential curve since 2000, about doubling every two years since then: $10 in 2000, 20 in '02, 40 in '04, about 80 in '06...
Now on top of that, we are starting to have feed back loops:
Export lands are starting to want to use much more of their own energy sources rather than sending them all over seas, at whatever price;
As these producers realize the price of this limited commodity is going to go up indefinitely, they will have better and better incentives to leave it in the ground ever longer since they can anticipate that it will be worth ever more in the future;
Other hording phenomena will soon kick in (note Bush's attempt to increase the Strategic Petroleum Reserve);
As Jack just pointed out, when traders start realizing that they are dealing with a commodity with real geological limits that are being reached, panic will set in, driving the price ever higher...
I'm sure some of you can think of other such feedback loops that have started or soon will kick in.
So when you add even one or two of these feedback loops onto an already exponential growth curve, you get hyperbolic growth, and it's not pretty. Basically, instead of doubling over a fixed period of time, the price increases a set amount over an ever shrinking period of time, till you reach infinity--that is until all trading of oil in dollars becomes impossible.
So if we take a couple weeks ago as our starting point for the sake of mathematical convenience, the price was about $120, about double what it was a year ago--an increase of $60 over a period of a year.
If this represent a blip from which it will return to its now "normal" exponential growth of doubling every two years, we should expect the price not to rise much above $160 this year not hit $320 till about 2010.
If this is a new level of exponential growth, then we will now see doubling every year.
Both of these scenarios are really bad, but I would now say that they represent wild-eyed, pollyannish optimism at this point--really bad, but still best-case scenarios.
Given the tendency mentioned above for added feedback loops to knock growth from exponential to hyperbolic, we should see another $60 rise in the next four months, and then another in the next two months--so another doubling over the next HALF-year.
But this is just the beginning. From there it would keep rising $60 at ever shrinking stretches of time: in about three weeks, in about two, in about ten days, nine, eight.... then two day, one day, and then it is increasing by $60 in less than a day, less that and hour, a minute....
By next year about this time, by these calculations, oil will not be purchasable by any quantity of dollars. Essentially this is hyperinflation of the dollar in relation to oil.
So that's my latest. I don't give the system more than about a year before oil becomes for all intents and purposes un-purchase-able by those holding any quantity of dollars.
Of course, it is unlikely to be a smooth ride up--there will be huge peaks and craters as people assume that oil can't go higher and cash out, only to find that oil does go up further and their cash is worthless.
I hope to heaven that I'm wrong, but this model points pretty strongly in the direction of total collapse within about a year.
But then again, maybe the magic of the market will solve everything afterall
Thoughts?
Here's a bit on feedback loops from Wikipedia (my emphasis):
"A system in equilibrium in which there is positive feedback to any change in its current state is said to be in an unstable equilibrium, whereas one with negative feedback is said to be in a stable equilibrium.
The end result of a positive feedback is often amplifying and "explosive", i.e. a small perturbation results in big changes. This feedback, in turn, will drive the system further away from its original setpoint, thus amplifying the original perturbation signal, and eventually become explosive because the amplification often grows exponentially (with the first order positive feedback),
or even hyperbolically (with the second order positive feedback). Indeed, chemical and nuclear fission based explosives offer an excellent physical demonstration of positive feedback. Bombarding fissile material with neutrons causes it to emit even more neutrons, which in turn affect the material. The greater the mass of fissile material, the larger the amplification, resulting in greater feedback. If the amplification is great enough, the process accelerates until the fissile material is spent or dispersed by the resulting explosion."
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